Rotational varifocal planar lens

ABSTRACT

A varifocal lens includes a first phase plate and a second phase plate which are rotatable relative to each other about an optical axis. The first phase plate includes a plurality of first phase conversion elements, the second phase plate includes a plurality of second phase conversion elements, and the plurality of first phase conversion elements and the plurality of second phase conversion elements are arranged so that light transmitted through the first phase plate and the second phase plate is focused on different positions on the optical axis depending on a relative rotational displacement between the first phase plate and the second phase plate.

CROSS-REFERENCE TO RELATED APPLICATION

This is a continuation of U.S. application Ser. No. 15/692,537 filed onAug. 31, 2017, which claims priority from Korean Patent Application No.10-2016-0127546, filed on Oct. 4, 2016 in the Korean IntellectualProperty Office, the disclosures of which are incorporated herein intheir entirety by reference.

BACKGROUND 1. Field

Apparatuses consistent with the present disclosure relate to varifocallenses in which focus changes as focal length changes, and moreparticularly, to rotational varifocal planar lenses capable of beingfabricated in a planar form with a small thickness.

2. Description of the Related Art

Similar to compact cameras and cameras for mobile devices, mirrorlesscameras and single-lens reflex cameras being fabricated to have smallersizes. Accordingly, lenses for small cameras are required. Until now,most lenses for small cameras have been designed as fixed focus lenses,that is, lenses with a fixed focal length. However, since the angle ofview of the fixed focal length lens is fixed, it is difficult to take apicture with various effects. In particular, compact cameras or camerasfor mobile devices are generally designed to be suitable for close-upphotography, and thus, may not be suitable for long-distancephotography.

A multifocal lens having multiple focal lengths or a zoom lens having avariable focal length is widely used as a lens for taking a picture fromboth a short distance away from the object being photographed and a longdistance away from the object being photographed. However, since thezoom lens is usually composed of a plurality of lens elements, a camerausing the zoom lens is long and heavy.

SUMMARY

Exemplary embodiments provide varifocal lenses including a first phaseplate and a second phase plate which are rotatable relative to eachother about an optical axis.

According to an aspect of an exemplary embodiment, there is provided afirst phase plate including a plurality of first phase conversionelements, at least some of the plurality of first phase conversionelements having diameters that are different from each other; and asecond phase plate including a plurality of second phase conversionelements, at least some of the plurality of first phase conversionelements having diameters that are different from each other, whereinthe first phase plate and the second phase plate face each other alongan optical axis and are rotatable relative to each other about theoptical axis to create relative rotational displacement between thefirst phase plate and the second phase plate, and the plurality of firstphase conversion elements and the plurality of second phase conversionelements are configured so that light transmitted through the firstphase plate and the second phase plate is focused on different positionson the optical axis depending on the relative rotational displacementbetween the first phase plate and the second phase plate.

The plurality of first phase conversion elements and the plurality ofsecond phase conversion elements may have radially symmetric columnshapes, wherein the plurality of first phase conversion elements mayhave different diameters from each other depending on positions of theplurality of first phase conversion elements on the first phase plate sothat a phase of light transmitted through the first phase plate changesdifferently depending on the positions of the plurality of first phaseconversion elements on the first phase plate, and the plurality ofsecond phase conversion elements may have different diameters from eachother depending on positions of the plurality of second phase conversionelements on the second phase plate so that a phase of light transmittedthrough the second phase plate changes differently depending on thepositions of the plurality of second phase conversion elements on thesecond phase plate.

The diameters of the plurality of first phase conversion elementsaccording to the positions of the plurality of first phase conversionelements on the first phase plate and the diameters of the plurality ofsecond phase conversion elements according to the positions of theplurality of second phase conversion elements on the second phase platemay be determined so that the phase of light transmitted through each ofthe first phase plate and the second phase plate is proportional to asquare of a radial distance with respect to the optical axis andproportional to an azimuth angle.

Each of the first phase plate and the second phase plate may bespatially divided into at least two regions in at least one of anazimuth direction and a radial direction, and the plurality of firstphase conversion elements may be arranged in the at least two regions ofthe first phase plate and the plurality of second phase conversionelements may be arranged in the at least two regions of the second phaseplate so that the at least two regions of each of the first phase plateand the second phase plate have operating wavelengths that are differentfrom each other.

Thicknesses of the plurality of first phase conversion elements may beequal to thicknesses of the plurality of second phase conversionelements.

The first phase plate may further include a first substrate that istransparent and the plurality of first phase conversion elements arearranged on the first substrate at regular intervals in a square latticeor hexagonal lattice shape, and the second phase plate may furtherinclude a second substrate that is transparent and the plurality ofsecond phase conversion elements are arranged on the second substrate atregular intervals in a square lattice or hexagonal lattice shape.

A space between the plurality of first phase conversion elements and aspace between the plurality of second phase conversion elements may beless than an operating wavelength.

Each of the plurality of first phase conversion elements and each of theplurality of second phase conversion elements may include a materialhaving a refractive index higher than that of the first substrate andthe second substrate.

Each of the first substrate and the second substrate may have a flatplate shape, and the first phase plate and the second phase plate may bearranged so that the plurality of first phase conversion elements andthe plurality of second phase conversion elements face each other.

The first phase plate may further include a first dielectric layerprovided on the first substrate and filling spaces between the pluralityof first phase conversion elements, the second phase plate may furtherinclude a second dielectric layer provided on the second substrate andfilling spaces between the plurality of second phase conversionelements, and each of the first dielectric layer and the seconddielectric layer may be transparent.

A thickness of the first dielectric layer may be greater thanthicknesses of the plurality of first phase conversion elements so thatthe first dielectric layer completely covers the plurality of firstphase conversion elements, and a thickness of the second dielectriclayer may be greater than thicknesses of the plurality of second phaseconversion elements so that the second dielectric layer completelycovers the plurality of second phase conversion elements.

The first phase plate and the second phase plate may be arranged so thatthe first dielectric layer and the second dielectric layer are incontact with each other.

When the relative rotational displacement between the first phase plateand the second phase plate is 0, a refractive power of the varifocallens may be greater than 0, and the plurality of first phase conversionelements and the plurality of second phase conversion elements may bearranged so that the refractive power of the varifocal lens isproportional to the relative rotational displacement between the firstphase plate and the second phase plate.

The varifocal lens may further include: a third phase plate including aplurality of third phase conversion elements, at least some of theplurality of third phase conversion elements having diameters that aredifferent from each other; and a fourth phase plate including aplurality of fourth phase conversion elements, at least some of theplurality of fourth phase conversion elements having diameters that aredifferent from each other, wherein the plurality of first phaseconversion elements and the plurality of second phase conversionelements are configured so that the first phase plate and the secondphase plate collectively function as a first lens element, and theplurality of third phase conversion elements and the plurality of fourthphase conversion elements are configured so that the third phase plateand the fourth phase plate collectively function as a second lenselement.

The first phase plate, the second phase plate, the third phase plate,and the fourth phase plate may be sequentially arranged along theoptical axis, the third phase plate and the fourth phase plate may berotatable relative to each other about the optical axis to createrelative rotational displacement between the third phase plate and thefourth phase plate, and the plurality of third phase conversion elementsand the plurality of fourth phase conversion elements may be configuredso that light transmitted through the third phase plate and the fourthphase plate is focused on different positions on the optical axisdepending on the relative rotational displacement between the thirdphase plate and the fourth phase plate.

Each of the plurality of third phase conversion elements and each of theplurality of fourth phase conversion elements may have a radiallysymmetric column shape, the plurality of third phase conversion elementsmay have different diameters from one another depending on positions ofthe plurality of third phase conversion elements on the third phaseplate so that a phase of light transmitted through the third phase platechanges differently depending on the positions of the plurality of thirdphase conversion elements on the third phase plate, and the plurality offourth phase conversion elements may have different diameters from oneanother depending on positions of the plurality of fourth phaseconversion elements on the fourth phase plate so that a phase of lighttransmitted through the fourth phase plate changes differently dependingon the positions of the plurality of fourth phase conversion elements onthe fourth phase plate.

The diameters of the plurality of third phase conversion elementsaccording to the positions of the plurality of third phase conversionelements on the third phase plate and the diameters of the plurality offourth phase conversion elements according to the positions of theplurality of fourth phase conversion elements on the fourth phase platemay be determined so that the phase of light transmitted through each ofthe third phase plate and the fourth phase plate is proportional to asquare of a radial distance with respect to the optical axis andproportional to an azimuth angle.

The first lens element and the second lens element may have refractivepowers with a same sign, and the plurality of first phase conversionelements, the plurality of second phase conversion elements, theplurality of third phase conversion elements, and the plurality offourth phase conversion elements may be arranged so that a degree ofchange of a refractive power of the first lens element with respect tothe relative rotational displacement between the first phase plate andthe second phase plate is equal to a degree of change of a refractivepower of the second lens element with respect to relative rotationaldisplacement between the third phase plate and the fourth phase plate.

The plurality of first phase conversion elements, the plurality ofsecond phase conversion elements, the plurality of third phaseconversion elements, and the plurality of fourth phase conversionelements may be arranged so that the first lens element and the secondlens element have refractive powers with opposite signs, the pluralityof first phase conversion elements and the plurality of second phaseconversion elements are arranged in a same form, and the plurality ofthird phase conversion elements and the plurality of fourth phaseconversion elements are arranged in a same form.

The first lens element and the second lens element may have refractivepowers with a same sign, and the plurality of first phase conversionelements, the plurality of second phase conversion elements, theplurality of third phase conversion elements, and the plurality offourth phase conversion elements are arranged so that a degree of changeof a refractive power of the first lens element with respect to therelative rotational displacement between the first phase plate and thesecond phase plate is different from a degree of change of a refractivepower of the second lens element with respect to relative rotationaldisplacement between the third phase plate and the fourth phase plate.

According to an aspect of another exemplary embodiment, there isprovided an image acquisition device including: a varifocal lensincluding a first phase plate including a plurality of first phaseconversion elements, at least some of the plurality of first phaseconversion elements having diameters that are different from each other,and a second phase plate including a plurality of second phaseconversion elements, at least some of the plurality of second phaseconversion elements having diameters that are different from each other;an actuator configured to rotationally displace the first phase plateand the second phase plate relative to each other; a controllerconfigured to control the actuator to create a relative rotationaldisplacement between the first phase plate and the second phase plate;and an image pickup device, wherein the first phase plate and the secondphase plate face each other along an optical axis and are rotatablerelative to each other about the optical axis, and the plurality offirst phase conversion elements and the plurality of second phaseconversion elements are arranged so that light transmitted through thefirst phase plate and the second phase plate is focused on differentpositions on the optical axis depending on the relative rotationaldisplacement between the first phase plate and the second phase plate.

Additional aspects will be set forth in part in the description whichfollows and, in part, will be apparent from the description, or may belearned by practice of the presented embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and/or other aspects will become apparent and more readilyappreciated from the following description of exemplary embodiments,taken in conjunction with the accompanying drawings in which:

FIG. 1 is a cross-sectional view of a varifocal lens according to anexemplary embodiment;

FIG. 2 is a perspective view of a phase plate of the varifocal lensshown in FIG. 1;

FIG. 3 is a graph illustrating a relationship between a diameter of oneof phase conversion elements arranged in a phase plate and a phasechange of transmitted light;

FIG. 4 is a plan view illustrating an arrangement of a plurality offirst phase conversion elements of a first phase plate, according to anexemplary embodiment;

FIG. 5 is a graph showing a relationship between a rotationaldisplacement between a first phase plate and a second phase plate and arefractive power of a varifocal lens;

FIG. 6 is a graph showing a relationship between the rotationaldisplacement between a first phase plate and a second phase plate and arefractive power of a varifocal lens, according to another exemplaryembodiment;

FIG. 7 is a cross-sectional view of a varifocal lens according toanother exemplary embodiment;

FIG. 8 is a cross-sectional view of a varifocal lens according toanother exemplary embodiment, which include two lens elements;

FIG. 9 is a cross-sectional view showing a configuration of an opticallens equivalent to a varifocal lens when two lens elements are the same;

FIG. 10 is a graph showing a relationship between a rotationaldisplacements between a first phase plate and a second phase plate andbetween a third phase plate and a fourth phase plate and a refractivepower of the varifocal lens, with respect to the example of FIG. 9;

FIG. 11 is a cross-sectional view showing a configuration of an opticallens equivalent to a varifocal lens when signs of the refractive powersof two lens elements are opposite each other;

FIG. 12 is a graph showing a relationship between rotationaldisplacements between a first phase plate and a second phase plate andbetween a third phase plate and a fourth phase plate and the refractivepower of the varifocal lens, with respect to the example of FIG. 11;

FIG. 13 is a cross-sectional view showing a configuration of an opticallens equivalent to a varifocal lens when the signs of the refractivepowers of two lens elements are the same and the magnitudes of therefractive powers are different from each other;

FIG. 14 is a graph showing a relationship between rotationaldisplacements between a first phase plate and a second phase plate andbetween a third phase plate and a fourth phase plate and the refractivepower of the varifocal lens, with respect to the example of FIG. 13;

FIGS. 15 and 16 are plan views showing configurations of a first phaseplate according to another exemplary embodiment; and

FIG. 17 is a conceptual diagram of an image acquisition apparatusaccording to an exemplary embodiment.

DETAILED DESCRIPTION

Hereinafter, with reference to the accompanying drawings, exemplaryembodiments will be described in detail. Like reference numerals referto like elements throughout, and in the drawings, sizes of elements maybe exaggerated for clarity and convenience of explanation. Theembodiments described below are merely exemplary, and variousmodifications may be possible from the embodiments. In a layer structuredescribed below, an expression such as “above” or “on” may include notonly the meaning of “immediately on/under/to the left/to the right in acontact manner”, but also the meaning of “on/under/to the left/to theright in a non-contact manner”.

FIG. 1 is a cross-sectional view of a varifocal lens 100 according to anexemplary embodiment. Referring to FIG. 1, the varifocal lens 100according to the exemplary embodiment may include a first phase plate110 and a second phase plate 120 arranged to face each other along anoptical axis OX and configured to be rotatable relative to each otherabout the optical axis OX. The first phase plate 110 may include a firstsubstrate 111, which is transparent, and a plurality of first phaseconversion elements 112 arranged two-dimensionally on a surface of thefirst substrate 111 facing the second phase plate 120. The second phaseplate 120 may include a second substrate 121, which is transparent, anda plurality of second phase conversion elements 122 arrangedtwo-dimensionally on a surface of the second substrate 121 facing thefirst phase plate 110. That is, the first phase plate 110 and the secondphase plate 120 may be arranged so that the first phase conversionelements 112 and the second phase conversion elements 122 face eachother. The first phase conversion elements 112 and the second phaseconversion elements 122 may not be in contact with each other so thatdamage does not occur when the first phase plate 110 and the secondphase plate 120 rotate relative to each other. According to an exemplaryembodiment, the first phase conversion element 112 and the second phaseconversion element 122 may be spaced apart from each other by a distanceg.

The first phase conversion element 112 and the second phase conversionelement 122 may protrude above the surface of the first substrate 111and the surface of the second substrate 121, respectively. For example,FIG. 2 is a perspective view of the first phase plate 110 of thevarifocal lens 100 shown in FIG. 1. As shown in FIG. 2, the first phaseconversion elements 112 may be two-dimensionally arranged on the firstsubstrate 111 to form a predetermined pattern. For example, the firstphase conversion elements 112 may be arranged at regular intervals inthe form of a square lattice or hexagonal lattice, and the second phaseconversion elements 122 may also be arranged in the form of a squarelattice or hexagonal lattice. Here, the interval between adjacent firstphase conversion elements 112 or the period of arrangement of the firstphase conversion elements 112 may be less than an operating wavelengthof the varifocal lens 100. By reducing the interval between the adjacentfirst phase conversion elements 112, it is possible to suppress thegeneration of a higher order diffraction component.

Each of the first phase conversion elements 112 may have, for example, acylindrical shape. Each of the second phase conversion elements 122 mayalso have a cylindrical shape. However, the first and second phaseconversion elements 112 and 122 do not necessarily have to have acylindrical shape, but instead may have the form of a radially symmetricpolygonal column, such as a square column or a hexagonal column. Thefirst and second phase conversion elements 112 and 122 may be formedusing a general semiconductor patterning process, although are notlimited thereto and may also be formed using many other types ofprocesses. For example, after stacking the material layers of the firstand second phase conversion elements 112 and 122 on the surfaces of thefirst and second substrates 111 and 121, respectively, the first andsecond phase conversion elements 112 and 122 may be formed simply bypatterning the material layers by using a photolithography process orsome other type of process known to those skilled in the art.

The first substrate 111 and the second substrate 121 may include, forexample, a transparent glass plate, a transparent plastic material or acombination thereof. The first and second phase conversion elements 112and 122 may include a material having a refractive index higher than arefractive index of a material of the first and second substrates 111and 121. For example, the first and second phase conversion elements 112and 122 may include a high refractive index material, such as germanium(Ge), amorphous silicon (a-Si), polycrystalline silicon (p-Si),monocrystalline silicon (c-Si), group III-V compound, TiO₂, or SiNx,although they are not limited thereto. For example, the refractive indexof the first and second phase conversion elements 112 and 122 may begreater than 3.5 at a visible light wavelength. It is understood, ofcourse, that the refractive index of the first and second phaseconversion elements 112 and 122 may also be equal to or less than 3.5.

When incident light passes through the first and second phase conversionelements 112 and 122 having the high refractive indexes, the phase ofthe incident light is delayed by the first and second phase conversionelements 112 and 122, and the phase of a transmitted light transmittedthrough the first and second phase conversion elements 112 and 122 isdifferent from the phase of the incident light. The extent to which thephase of the incident light changes may be determined depending on thesizes and the thicknesses t of the first and second phase conversionelements 112 and 122. If the first and second phase conversion elements112 and 122 have, for example, a shape of the form of a polygonalcolumn, the phase of the transmitted light changes depending on thediameters d and the thicknesses t of the first and second phaseconversion elements 112 and 122.

For example, FIG. 3 is a graph illustrating the relationship between thediameter of one of the first and second phase conversion elements 112and 122, respectively arranged in the first and second phase plates 110and 120, and a phase change of the transmitted light. In the graph ofFIG. 3, it is assumed that each of the first and second phase conversionelements 112 and 122 has the form of a cylinder including amorphoussilicon, is arranged in the form of a hexagonal lattice with a period of650 nm, and has a thickness of 715 nm. In addition, it is assumed thatthe wavelength of the incident light is 950 nm. However, exemplaryembodiments are not limited thereto. For example, the first and secondphase conversion elements 112 and 122 may include materials other than,or in addition to, amorphous silicon, and may have a period of more orless than 650 nm and a thickness of more or less than 715 nm. Referringto FIG. 3, the diameters of the first and second phase conversionelements 112 and 122 and the phase change are not linearly related butnonlinearly related. However, it may be understood that the phase changeincreases as the diameters of the first and second phase conversionelements 112 and 122 increases.

Accordingly, when at least some of the first and second phase conversionelements 112 and 122 have different sizes or different thicknesses, thetransmitted light transmitted through the first and second phase plates110 and 120 may have different phases depending on local positions ofthe first and second phase conversion elements 112 and 122 on the firstand second plates 110 and 120. That is, the phase of the transmittedlight changes locally depending on the positions of the first and secondphase conversion elements 112 and 122 on the first and second phaseplates 110 and 120. By appropriately arranging the plurality of firstand second phase conversion elements 112 and 122 having different sizesor different thicknesses, it is possible to control, as desired, thewave front of the transmitted light transmitted through the first andsecond phase plates 110 and 120. For example, depending on thearrangement of the first and second phase conversion elements 112 and122, the first and second phase plates 110 and 120 may serve asrefractive optical elements such as lenses. The first and second phaseplates 110 and 120 may also serve as other types of optical elements inaddition to or instead of lenses.

According to the present exemplary embodiment, the arrangement of thefirst and second phase conversion elements 112 and 122 may be designedso that the phase distribution of the transmitted light transmittedthrough the first and second phase plates 110 and 120 is proportional tothe product of the square of a radial distance from the optical axis OXand an azimuth angle, as shown in Equation 1, and the first phase plate110 and the second phase may be disposed to face each other. In Equation1, ϕ represents a phase change of transmitted light, r represents aradial distance from an optical axis OX, 8 represents an azimuth angle,and a represents a proportional constant.

ϕ=aθr ²  [Equation 1]

Then, when the first phase plate 110 and the second phase plate 120 arerotated relative to each other about the optical axis OX, the totalphase change of the varifocal lens 100, which is caused by a combinationof the first phase plate 110 and the second phase plate 120, variesdepending on the relative rotational displacement between the firstphase plate 110 and the second phase plate 120. For example, therefractive power of the varifocal lens 100 may be changed according tothe relative rotational displacement and the displacement direction ofthe first phase plate 110 and the second phase plate 120 so that thefocal length of the varifocal lens 100 is changed. To this end, thefirst and second phase conversion elements 111 and 122 may be arrangedso that light transmitted through the first phase plate 110 and thesecond phase plate 120 is focused on different positions on the opticalaxis OX according to the relative rotational displacement between thefirst phase plate 110 and the second phase plate 120. That is, the firstand second phase conversion elements 112 and 122 may be arranged so thatthe phase distribution of the transmitted light transmitted through thefirst and second phase plates 110 and 120 is as shown in Equation 1.

For example, FIG. 4 is a plan view illustrating the arrangement of aplurality of first phase conversion elements 112 of the first phaseplate 110, according to an exemplary embodiment. Referring to FIG. 4,the plurality of first phase conversion elements 112 have differentdiameters depending on their positions on the first phase plate 110 sothat the phase of light transmitted through the first phase plate 110changes differently depending on the positions of the first phaseconversion elements 112 on the first phase plate 110. The second phaseplate 120 may also be designed in the same manner as the phase plate110. That is, the plurality of second phase conversion elements 122 mayhave different diameters depending on their local positions on thesecond phase plate 120 so that the phase of light transmitted throughthe second phase plate 120 changes differently depending on their localpositions on the second phase plate 120. The diameters of the firstphase conversion elements 112 are illustratively shown in FIG. 4. Thediameters of the plurality of first phase conversion elements 112, whichare different from each other depending on their positions on the firstphase plate 110, may be selected so that the phase of light transmittedthrough the first phase plate 110 satisfies a condition as shown inEquation 1. Similarly, the diameters of the plurality of second phaseconversion elements 122, which are different from each other dependingon their positions on the second phase plate 120, may be selected sothat the phase of light transmitted through the second phase plate 120satisfies a condition as shown in Equation 1.

When the phase change ϕ at a position of each of the first and secondphase plates 110 and 120 is determined, the diameters of the first andsecond phase conversion elements 112 and 122 at the respective positionsof the first and second phase plates 110 and 120 may be determined basedon the relationship between the diameters of the first and second phaseconversion elements 112 and 122 and a phase change of transmitted light,illustrated in FIG. 3. The phase change of the transmitted light may beaffected by the thicknesses of the first and second phase conversionelements 112 and 122. However, when the thicknesses of the first andsecond phase conversion elements 112 and 122 are different from eachother, a process of manufacturing the first and second phase plates 110and 120 may be complicated, and thus, for example, the first and secondphase conversion elements 112 and 122 may be formed to have the samethickness of 715 nm.

FIG. 5 is a graph showing the relationship between the rotationaldisplacement between the first phase plate 110 and the second phaseplate 120 and the refractive power of the varifocal lens 100 in the casein which the arrangement of the first phase conversion elements 112 ofthe first phase plate 110 and the arrangement of the second phaseconversion elements 122 of the second phase plate 120 are identical toeach other. Referring to FIG. 5, it may be understood that therefractive power of the varifocal lens 100 has a linear proportionalrelation to the rotational displacement. For example, when therotational displacement is 0, the varifocal lens 100 has a refractivepower of 0, and as the rotational displacement increases or decreases,the refractive power of the varifocal lens 100 may also increase ordecrease in proportion thereto. The focal length of the varifocal lens100 may be represented as shown in Equation 2 as the reciprocal of therefractive power.

$\begin{matrix}{f^{- 1} = \frac{a\; \theta_{rot}\lambda}{\pi}} & \lbrack {{Equation}\mspace{14mu} 2} \rbrack\end{matrix}$

In Equation 2, f represents a focal length, θ_(rot) representsrotational displacement, λ represents the wavelength of incident light,and a represent a proportional constant as shown in Equation 1. Therefractive power f⁻¹ may be proportional to the rotational displacementθ_(rot), as shown in Equation 2. Optical characteristics of thevarifocal lens 100 may be determined mainly by the proportional constanta. For example, if the proportional constant a is a positive number, thevarifocal lens 100 may have a positive refractive power when positiverotational displacement occurs, and as the magnitude of the proportionalconstant increases, a change in the refractive power due to therotational displacement may also increase. Therefore, after theproportional constant a is determined depending on desiredcharacteristics of the varifocal lens 100, the arrangement of the firstphase conversion elements 112 and the second phase conversion elements122 may be designed to satisfy the condition of Equation 1.

In the example of FIG. 5, the refractive power is 0 when the rotationaldisplacement is 0. However, an initial offset value may be given so asto have a refractive power even when there is no rotationaldisplacement. FIG. 6 is a graph showing the relationship between therotational displacement between the first phase plate 110 and the secondphase plate 120 and the refractive power of the varifocal lens 100,according to another exemplary embodiment. Referring to FIG. 6, thevarifocal lens 100 has a refractive power greater than 0 when therotational displacement is 0. As the relative rotational displacementbetween the first phase plate 110 and the second phase plate 120increases or decreases, the refractive power may increase or decrease inproportion thereto. For example, when the rotational displacement is 0,the arrangement of the first phase conversion elements 112 and thearrangement of the second phase conversion elements 112 may be designedso that the second phase conversion elements 122 are rotated by theinitial offset value with respect to the first phase conversion elements112.

The varifocal lens 100 according to the present exemplary embodiment maybe formed in a planar shape and thus may have a small thickness. Forexample, the varifocal lens 100 may have a small thickness of several umto several mm. Thus, the varifocal lens 100 may provide a zoom functionto a compact camera or a camera for a mobile device. In addition, sincethe varifocal lens 100 according to the present exemplary embodiment maybe manufactured by a patterning method using a photolithography process,a complicated processing step for forming a complex curved surface of anoptical lens element is not required. Accordingly, the varifocal lens100 may be easily manufactured and quality deterioration due to aprocess error may be reduced, and thus, image quality may be improved.Furthermore, since the refractive power may be changed by simplyrotating the first phase plate 110 or the second phase plate 120, it isnot necessary to secure an additional space for adjusting the refractivepower. Also, since a phase change is given in the form of a quadraticpolynomial with respect to a radial distance, as shown in Equation 1, aphase distribution change at a position away from the optical axis OX isrelatively small. Therefore, it is easy to design a varifocal lenshaving a large diameter.

FIG. 7 is a cross-sectional view of a varifocal lens 200 according toanother exemplary embodiment. Referring to FIG. 7, the varifocal lens200 may further include first and second dielectric layers 113 and 123that are transparent and surround and protect first and second phaseconversion elements 112 and 122. For example, a first phase plate 110may include the first dielectric layer 113 filled between a plurality offirst phase conversion elements 112, and a second phase plate 120 mayinclude the second dielectric layer 123 filled between a plurality ofsecond phase conversion elements 122. The first and second dielectriclayers 113 and 123 may include a material such as siloxane-based spin onglass (SAG), transparent polymer material, SiO₂, or the like.

In order to sufficiently protect the first and second phase conversionelements 112 and 122, the thickness of the first dielectric layer 113may be greater than that of the first phase conversion element 112 tocompletely cover the first phase conversion element 112, and thethickness of the second dielectric layer 123 may be greater than that ofthe second phase conversion element 122 to completely cover the secondphase conversion element 122. In this case, the first and second phaseconversion elements 112 and 122 may not be damaged when the first phaseplate 110 and the second phase plate 120 are relatively rotated.Accordingly, as shown in FIG. 7, the first phase plate 110 and thesecond phase plate 120 may be disposed so that the first dielectriclayer 113 and the second dielectric layer 123 are in contact with eachother.

FIG. 8 is a cross-sectional view of a varifocal lens 300 according toanother exemplary embodiment. Referring to FIG. 8, the varifocal lens300 may further include a third phase plate 130 and a fourth phase plate140 in addition to a first phase plate 110 and a second phase plate 120.For example, the first phase plate 110 to the fourth phase plate 140 maybe sequentially disposed along an optical axis. The third phase plate130 may include a third substrate 131, a plurality of third phaseconversion elements 132 having different sizes, and a third dielectriclayer 133 for protecting the third phase conversion elements 132. Thefourth phase plate 140 may include a fourth substrate 141, a pluralityof fourth phase conversion elements 142 having different sizes, and afourth dielectric layer 143 for protecting the fourth phase conversionelements 142.

A plurality of first phase conversion elements 112 and a plurality ofsecond phase conversion elements 122 may be arranged so that a pair ofthe first and second phase plates 110 and 120 functions as a first lenselement. A plurality of third phase conversion elements 132 and aplurality of fourth phase conversion elements 142 may be arranged sothat a pair of the third and fourth phase plates 130 and 140 functionsas a second lens element. The first phase plate 110 and the second phaseplate 120 may be configured to be rotatable relative to each other aboutthe optical axis, and the third phase plate 130 and the fourth phaseplate 140 may be configured to be rotatable relative to each other inthe direction perpendicular to the optical axis. The first and secondphase conversion elements 112 and 122 may be arranged so that lighttransmitted through the first phase plate 110 and the second phase plate120 is focused on different positions on the optical axis depending onthe relative rotational displacement between the first phase plate 110and the second phase plate 120. Similarly, the third and fourth phaseconversion elements 132 and 142 may be arranged so that lighttransmitted through the third phase plate 130 and the fourth phase plate140 is focused on different positions on the optical axis depending onthe relative rotational displacement between the third phase plate 130and the fourth phase plate 140. Accordingly, the focal length of thevarifocal lens 300 may vary depending on the relative rotationaldisplacement between the first phase plate 110 and the second phaseplate 120 and the relative rotational displacement between the thirdphase plate 130 and the fourth phase plate 140.

As described above with reference to FIGS. 2 and 3, the first to fourthphase conversion elements 112, 122, 132, and 142 may have the form of acylindrical or polygonal column with a radially symmetric shape. Thefirst to fourth phase conversion elements 112, 122, 132, and 142 mayhave different diameters depending on local positions on the first tofourth phase plates 110, 120, 130, and 140, respectively, so that thephase of light transmitted through the first to fourth phase plates 110,120, 130 and 140 changes differently depending on the local positions onthe first to fourth phase plates 110, 120, 130, and 140. For example,the diameters of the first and second phase conversion elements 112 and122 may be selected so that the phase of light transmitted through eachof the first and second phase plates 110 and 120 is proportional to thesquare of a radial distance about the optical axis and is proportionalto an azimuth angle. Similarly, the diameters of the third phaseconversion elements 132 according to their positions on the third phaseplate 130 and the diameters of the fourth phase conversion elements 142according to their positions on the fourth phase plate 140 may bedetermined so that the phase of light transmitted through each of thethird and fourth phase plates 130 and 140 is proportional to the squareof the radial distance about the optical axis and proportional to theazimuth angle.

In the varifocal lens 300 according to the present exemplary embodiment,the first lens element including the pair of the first and second phaseplates 110 and 120 and the second lens element including the pair of thethird and fourth phase plates 130 and 140 may be designed to have thesame optical characteristics or may be designed to have differentoptical characteristics.

For example, FIG. 9 is a cross-sectional view showing a configuration ofan optical lens equivalent to the varifocal lens 300 when two lenselements, i.e., first and second lens elements, are the same, and FIG.10 is a graph showing the relationship between the rotationaldisplacements between the first phase plate 110 and the second phaseplate 120 and between the third phase plate 130 and the fourth phaseplate 140 and the refractive power of the varifocal lens 300. Referringto FIG. 9, both the first lens element and the second lens element aredesigned to have a positive refractive power like a convex lens. Thedegree of change of the refractive power of the first lens element withrespect to the relative rotational displacement between the first phaseplate 110 and the second phase plate 120 is equal to the degree ofchange of the refractive power of the second lens element with respectto the relative rotational displacement between the third phase plate130 and the fourth phase plate 140. To this end, the proportionalconstant a of Equation 1 may be selected equally for the first lenselement and the second lens element. For example, the first to fourthphase conversion elements 112, 122, 132, and 142 may all be arranged inthe same form.

Referring to FIG. 10, a line indicated by ‘A’ represents a change in therefractive power of each of the first lens element and the second lenselement, and a line indicated by ‘B’ represents the overall change inthe refractive power of the varifocal lens 300. As shown in FIG. 10, theoverall change in the refractive power of the varifocal lens 300 is thesum of the change in the refractive power of the first lens element andthe change in the refractive power of the second lens element.Therefore, the range of change in the refractive power of the varifocallens 300 may be increased. In general, even if the proportional constanta is increased, a large refractive power change may be obtained.However, if the proportion constant a increases, a phase change rapidlyincreases at the edge of a phase plate, and thus, it may be difficult todesign and manufacture phase conversion elements. Therefore, when thetwo lens elements are combined as shown in FIG. 9, it is possible toincrease a change in the refractive power of the varifocal lens 300 in arange in which phase conversion elements may be designed andmanufactured.

FIG. 11 is a cross-sectional view showing a configuration of an opticallens equivalent to the varifocal lens 300 when the signs of therefractive powers of two lens elements, i.e., first and second elements,are opposite to each other, and FIG. 12 is a graph showing therelationship between the rotational displacements between the firstphase plate 110 and the second phase plate 120 and between the thirdphase plate 130 and the fourth phase plate 140 and the refractive powerof the varifocal lens 300, with respect to the example of FIG. 11.Referring to FIG. 11, the first lens element is designed to have anegative refractive power like a concave lens, and the second lenselement is designed to have a positive refractive power likes a convexlens. The degree of change of the refractive power of the first lenselement with respect to the relative rotational displacement between thefirst phase plate 110 and the second phase plate 120 may be equal to ordifferent from the degree of change of the refractive power of thesecond lens element with respect to the relative rotational displacementbetween the third phase plate 130 and the fourth phase plate 140. Tothis end, the proportional constant a for the first lens element mayhave a positive value, and the proportional constant a for the secondlens element may have a negative value.

Referring to FIG. 12, a line indicated by ‘A’ represents a change in therefractive power of the first lens element, a line indicated by ‘B’represents a change in the refractive power of the second lens element,and a line indicated by ‘C’ represents the overall change in therefractive power of the varifocal lens 300. With such a configuration,the aberration of the varifocal lens 300 may be compensated for byappropriately adjusting the relative rotational displacement between thefirst phase plate 110 and the second phase plate 120 and the relativerotational displacement between the third phase plate 130 and the fourthphase plate 140.

FIG. 13 is a cross-sectional view showing a configuration of an opticallens equivalent to the varifocal lens 300 when the signs of therefractive powers of two lens elements, i.e., first and second lenselements, are the same and the magnitudes of the refractive powers aredifferent from each other, and FIG. 14 is a graph showing therelationship between the rotational displacements between the firstphase plate 110 and the second phase plate 120 and between the thirdphase plate 130 and the fourth phase plate 140 and the refractive powerof the varifocal lens 300, with respect to the example of FIG. 13.Referring to FIG. 13, both the first lens element and the second lenselement are designed to have a positive refractive power like a convexlens. The degree of change of the refractive power of the second lenselement with respect to the relative rotational displacement between thethird phase plate 130 and the fourth phase plate 140 may be greater thanthe degree of change of the refractive power of the first lens elementwith respect to the relative rotational displacement between the firstphase plate 110 and the second phase plate 120. To this end, both theproportional constant a for the first lens element and the proportionalconstant a for the second lens element may have positive values, and theproportional constant a for the second lens element may be greater thanthat for the first lens element.

In this configuration, the refractive power of the varifocal lens 300may be first adjusted in a large range by using the third phase plate130 and the fourth phase plate 140, and then may be finely adjusted byusing the first phase plate 110 and the second phase. Referring to FIG.14, a line indicated by ‘A’ represents a refractive power contributionof the second lens element to the varifocal lens 300, and a lineindicated by ‘B’ represents a refractive power contribution of the firstelement to the varifocal lens 300. For example, a change in therefractive power indicated by ‘A’ may be obtained by adjusting therelative rotational displacement between the third phase plate 130 andthe fourth phase plate 140 in a state where the relative rotationaldisplacement between the first phase plate 110 and the second phaseplate 120 is fixed. Then, the refractive power indicated by ‘B’ may befinely adjusted by additionally adjusting the relative rotationaldisplacement between the first phase plate 110 and the second phaseplate 120 in a state where the relative rotational displacement betweenthe third phase plate 130 and the fourth phase plate 140 is fixed.

As may be understood from Equation 2, the refractive powers or focallengths of the varifocal lenses 100, 200, and 300 are also affected bythe wavelength λ of incident light. Accordingly, the first, second,third, and fourth phase plates 110, 120, 130, and 140 may be spatiallydivided so that the varifocal lenses 100, 200, and 300 may have variousoperating wavelengths. For example, FIGS. 15 and 16 are plan viewsshowing configurations of a first phase plate 110 according to anotherexemplary embodiment. As shown in FIG. 15, the first phase plate 110 maybe spatially divided into a plurality of regions (at least two regions),i.e., first, second, third, fourth, and fifth regions 110 a, 110 b, 110c, 110 d, and 110 e in an azimuth direction. In addition, as shown inFIG. 16, the first phase plate 110 may be spatially divided into aplurality of regions (at least two regions), i.e., first, second, third,fourth, and fifth regions 110 a, 110 b, 110 c, 110 d, and 110 e in aradial direction. Alternatively, by combining the configuration of FIG.15 and the configuration of FIG. 16, the first phase plate 110 may bespatially divided both in the azimuth direction and in the radialdirection. Although the first phase plate 110 is shown in FIGS. 15 and16 as being divided into five regions, i.e., first to, second, third,fourth, and fifth regions, 110 a, 110 b, 110 c, 110 d and 110 e, by wayof example, the inventive concept is not limited thereto and the numberof division regions may be appropriately selected as needed. Inaddition, although only the first phase plate 110 is shown in FIGS. 15and 16, the second, third, and fourth phase plates 120, 130, and 140 mayalso be spatially divided in the same manner as the first phase plate110.

According to the present exemplary embodiment, the first, second, third,fourth, and fifth regions 110 a, 110 b, 110 c, 110 d, and 110 e may havedifferent operating wavelengths. In other words, the diameters of thefirst phase conversion elements 112 may be selected depending on a localposition in the first region 110 a so that the first region 110 a has afirst operating wavelength. The first phase conversion elements 112 maybe arranged in each of the second, third, fourth, and fifth regions 110b, 110 c, 110 d, and 110 e so that the second region 110 b has a secondoperating wavelength, the third region 110 c has a third operatingwavelength, the fourth region 110 d has a fourth operating wavelength,and the fifth region 110 e has a fifth operating wavelength. Forexample, in order to allow the varifocal lens 100 to have the samerefractive power or focal length with respect to the first to fifthoperating wavelengths, the first phase conversion elements 112 may bearranged differently in the first, second, third, fourth, and fifthregions 110 a, 110 b, 110 c, 110 d, and 110 e. To this end, theproportional constant a for each of the first, second, third, fourth,and fifth regions 110 a, 110 b, 110 c, 110 d, and 110 e may be selectedin inverse proportion to the operating wavelength thereof.

The varifocal lenses 100, 200, 300, and 400 described above may be usedin an image acquisition device such as a compact camera or a camera fora mobile device. For example, FIG. 17 is a conceptual diagram of animage acquisition apparatus 500 according to an exemplary embodiment.Referring to FIG. 17, the image acquisition apparatus 500 may includes avarifocal lens 200, a first actuator 531 for rotating a first phaseplate 110 of the varifocal lens 200, a second actuator 532 for rotatinga second phase plate 120 of the varifocal lens 200, a controller 520 forcontrolling the rotational displacement between the first phase plate110 and the second phase plate 120 by driving the first and secondactuators 531 and 532, and an image pickup device 510 having a pluralityof pixels for sensing light. Also, the image acquisition apparatus 500may further include an optical shutter 540 for transmitting or blockinglight as needed.

Although the varifocal lens 200 shown in FIG. 2 is illustrated in FIG.17 by way of example, the image acquisition apparatus 500 may includeother varifocal lenses 100 and 300. In addition, one of the first andsecond actuators 531 and 532 may be omitted in FIG. 17. In other words,both the first and second phase plates 110 and 120 may be rotated byusing both the first and second actuators 531 and 532, or only one ofthe phase plates 110 and 120 may be rotated by using only one of thefirst and second actuators 531 and 532. The first and second actuators531 and 532 may be electric devices using electrostatic force ormagnetic force, or may be mechanical devices. The controller 520 maycalculate rotational displacement to obtain a desired focal length ofthe varifocal lens 200 according to a pre-programmed program or a user'sselection, and may control the first and second actuators 531 and 532 torotate the first and second phase plates 110 and 120 by the calculatedrotational displacement.

In addition, the image acquisition apparatus 500 may use only thevarifocal lens 200, but may further include an additional optical lenselement 550. Although only one optical lens element 550 is illustratedin FIG. 17 by way of example, the image acquisition apparatus 500 mayuse two or more optical lens elements 550 and the varifocal lens 200together.

The image acquistion apparatus 500 may also perform a function of adepth sensor by taking a photograph while continuously adjusting thefocal length of the varifocal lens 200. For example, since the distanceof the subject varies depending on the focal length of the varifocallens 200, a plurality of images obtained by performing photographingwhile continuously changing the focal length from a minimum focal lengthto a maximum focal length distance may be used to generate a depth map.

When the first and second phase plates 110 and 120 of the varifocal lens200 are spatially divided as shown in FIG. 15 or 16, the optical shutter540 may operate to use only any one of the first, second, third, fourthand fifth regions 110 a, 110 b, 110 c, 110 d, and 110 e depending on thecontrol of the controller 520. For example, the optical shutter 540 maytransmit light toward only one of the first, second, third, fourth andfifth regions 110 a, 110 b, 110 c, 110 d, and 110 e and block lighttoward the remaining regions.

While the rotational varifocal planar lens described above has beenshown and described in connection with the exemplary embodimentsillustrated in the drawings, it will be understood by those of ordinaryskill in the art that various modifications and equivalent embodimentscan be made therefrom. Therefore, the disclosed exemplary embodimentsshould be considered in an illustrative sense rather than a restrictivesense. The range of the embodiments will be in the appended claims, andall of the differences in the equivalent range thereof should beunderstood to be included in the embodiments.

What is claimed is:
 1. A varifocal lens comprising: a first phase platecomprising a plurality of first phase conversion elements, at least someof the plurality of first phase conversion elements having diametersthat are different from each other; and a second phase plate comprisinga plurality of second phase conversion elements, at least some of theplurality of first phase conversion elements having diameters that aredifferent from each other, wherein the diameters of the plurality offirst phase conversion elements according to positions of the pluralityof first phase conversion elements on the first phase plate and thediameters of the plurality of second phase conversion elements accordingto positions of the plurality of second phase conversion elements on thesecond phase plate are determined so that a phase of light transmittedthrough each of the first phase plate and the second phase plate isproportional to a square of a radial distance with respect to an opticalaxis and proportional to an azimuth angle.
 2. The varifocal lens ofclaim 1, wherein the plurality of first phase conversion elements andthe plurality of second phase conversion elements have radiallysymmetric column shapes, wherein the plurality of first phase conversionelements have different diameters from each other depending on thepositions of the plurality of first phase conversion elements on thefirst phase plate so that the phase of light transmitted through thefirst phase plate changes differently depending on the positions of theplurality of first phase conversion elements on the first phase plate,and the plurality of second phase conversion elements have differentdiameters from each other depending on positions of the plurality ofsecond phase conversion elements on the second phase plate so that thephase of light transmitted through the second phase plate changesdifferently depending on the positions of the plurality of second phaseconversion elements on the second phase plate.
 3. The varifocal lens ofclaim 1, wherein each of the first phase plate and the second phaseplate is spatially divided into at least two regions in at least one ofan azimuth direction and a radial direction, and the plurality of firstphase conversion elements are arranged in the at least two regions ofthe first phase plate and the plurality of second phase conversionelements are arranged in the at least two regions of the second phaseplate so that the at least two regions of each of the first phase plateand the second phase plate have operating wavelengths that are differentfrom each other.
 4. The varifocal lens of claim 1, wherein thicknessesof the plurality of first phase conversion elements are equal tothicknesses of the plurality of second phase conversion elements.
 5. Thevarifocal lens of claim 1, wherein the first phase plate furthercomprises a first substrate that is transparent and the plurality offirst phase conversion elements are arranged on the first substrate atregular intervals in a square lattice or hexagonal lattice shape, andthe second phase plate further comprises a second substrate that istransparent and the plurality of second phase conversion elements arearranged on the second substrate at regular intervals in a squarelattice or hexagonal lattice shape.
 6. The varifocal lens of claim 5,wherein a space between the plurality of first phase conversion elementsand a space between the plurality of second phase conversion elementsare less than an operating wavelength.
 7. The varifocal lens of claim 5,wherein each of the plurality of first phase conversion elements andeach of the plurality of second phase conversion elements comprise amaterial having a refractive index higher than that of the firstsubstrate and the second substrate.
 8. The varifocal lens of claim 5,wherein each of the first substrate and the second substrate have a flatplate shape, and the first phase plate and the second phase plate arearranged so that the plurality of first phase conversion elements andthe plurality of second phase conversion elements face each other. 9.The varifocal lens of claim 5, wherein the first phase plate furthercomprises a first dielectric layer provided on the first substrate andfilling spaces between the plurality of first phase conversion elements,the second phase plate further comprises a second dielectric layerprovided on the second substrate and filling spaces between theplurality of second phase conversion elements, and each of the firstdielectric layer and the second dielectric layer are transparent. 10.The varifocal lens of claim 9, wherein a thickness of the firstdielectric layer is greater than thicknesses of the plurality of firstphase conversion elements so that the first dielectric layer completelycovers the plurality of first phase conversion elements, and a thicknessof the second dielectric layer is greater than thicknesses of theplurality of second phase conversion elements so that the seconddielectric layer completely covers the plurality of second phaseconversion elements.
 11. The varifocal lens of claim 10, wherein thefirst phase plate and the second phase plate are arranged so that thefirst dielectric layer and the second dielectric layer are in contactwith each other.
 12. The varifocal lens of claim 1, wherein the firstphase plate and the second phase plate face each other along the opticalaxis and are rotatable relative to each other about the optical axis tocreate relative rotational displacement between the first phase plateand the second phase plate, and the plurality of first phase conversionelements and the plurality of second phase conversion elements areconfigured so that light transmitted through the first phase plate andthe second phase plate is focused on different positions on the opticalaxis depending on the relative rotational displacement between the firstphase plate and the second phase plate.
 13. The varifocal lens of claim12, wherein when the relative rotational displacement between the firstphase plate and the second phase plate is 0, a refractive power of thevarifocal lens is greater than 0, and the plurality of first phaseconversion elements and the plurality of second phase conversionelements are arranged so that the refractive power of the varifocal lensis proportional to the relative rotational displacement between thefirst phase plate and the second phase plate.
 14. The varifocal lens ofclaim 1, further comprising: a third phase plate comprising a pluralityof third phase conversion elements, at least some of the plurality ofthird phase conversion elements having diameters that are different fromeach other; and a fourth phase plate including a plurality of fourthphase conversion elements, at least some of the plurality of fourthphase conversion elements having diameters that are different from eachother, wherein the plurality of first phase conversion elements and theplurality of second phase conversion elements are configured so that thefirst phase plate and the second phase plate collectively function as afirst lens element, and the plurality of third phase conversion elementsand the plurality of fourth phase conversion elements are configured sothat the third phase plate and the fourth phase plate collectivelyfunction as a second lens element.
 15. The varifocal lens of claim 14,wherein the diameters of the plurality of third phase conversionelements according to positions of the plurality of third phaseconversion elements on the third phase plate and the diameters of theplurality of fourth phase conversion elements according to positions ofthe plurality of fourth phase conversion elements on the fourth phaseplate are determined so that a phase of light transmitted through eachof the third phase plate and the fourth phase plate is proportional to asquare of a radial distance with respect to the optical axis andproportional to an azimuth angle.
 16. The varifocal lens of claim 15,wherein each of the plurality of third phase conversion elements andeach of the plurality of fourth phase conversion elements have aradially symmetric column shape, the plurality of third phase conversionelements have different diameters from one another depending onpositions of the plurality of third phase conversion elements on thethird phase plate so that the phase of light transmitted through thethird phase plate changes differently depending on the positions of theplurality of third phase conversion elements on the third phase plate,and the plurality of fourth phase conversion elements have differentdiameters from one another depending on positions of the plurality offourth phase conversion elements on the fourth phase plate so that thephase of light transmitted through the fourth phase plate changesdifferently depending on the positions of the plurality of fourth phaseconversion elements on the fourth phase plate.
 17. The varifocal lens ofclaim 14, wherein the first phase plate, the second phase plate, thethird phase plate, and the fourth phase plate are sequentially arrangedalong the optical axis, the third phase plate and the fourth phase plateare rotatable relative to each other about the optical axis to createrelative rotational displacement between the third phase plate and thefourth phase plate, and the plurality of third phase conversion elementsand the plurality of fourth phase conversion elements are configured sothat light transmitted through the third phase plate and the fourthphase plate is focused on different positions on the optical axisdepending on the relative rotational displacement between the thirdphase plate and the fourth phase plate.